Q4. Assertion: two sinusoidal voltages of the same frequency can be added by adding their phasors like vectors. Reason: the amplitudes and phases of such quantities combine in the same way as the projections of rotating vectors. Are both true, and does the reason explain the assertion?
Both are true, and the reason explains the assertion (NCERT footnote, page 181).
Q5. Two voltages of the same frequency have amplitudes 5.0 V and 12 V, with the second phasor 60° ahead of the first. Find the amplitude of their sum.
A2 = 5.02 + 122 + 2 × 5.0 × 12 × cos 60° = 25 + 144 + 60 = 229, so A ≈ 15.1 V (reasoned with the phasor rule, NCERT page 181).
Q6. The current in a circuit is i = 2.0 sin(ωt + π/3) A and the voltage is v = 10 sin ωt V. Which leads, and by how much? Describe the phasor diagram.
The current leads by π/3 (60°). The current phasor, 2.0 A long, is drawn 60° anticlockwise from the voltage phasor, 10 V long, and both rotate together at ω (reasoned from NCERT page 181).
Q7. How long after the voltage reaches its peak does the current reach its peak, if the current lags by π/2 at 50 Hz?
A lag of π/2 is a quarter of a period. The period is 1/50 s = 20 ms, so the current peaks 5 ms after the voltage (NCERT page 183).